Physics - Semester 2

Question 1

What is the Bohr model of the atom?

Answer 1

The Bohr model is a model of the atom with a positive nucleus and negative electrons orbiting them, and adjusts for the fact that orbits decay by quantising the orbits to specific values, and only allowing energy emissions when electrons change orbits

Question 2

What is the equation for the angular momentum in an electron orbit?

Answer 2

L=mvr=nh/2π

Question 3

What acts as the centripetal force during an electron orbit?

Answer 3

The electrostatic attraction between the electron and the nucleus is strong enough to prevent the electron from flying away due to its angular velocity.

Question 4

What is the equation for centripetal force and electrostatic attraction?

Answer 4

(mv^2)/r =1/(4πε_0 ) (e^2/(r^2 ))

Question 5

What are the equations for the kinetic and potential energy of an electron orbit?

Answer 5

Kinetic:
K= 1/2 mv_n^2= 1/(ε_0^2 ) ((me^4)/(8n^2 h2 ))

Potential:
U=−1/(4πε_0 ) (e^2/r_n )=−1/(ε_0^2 ) ((me^4)/(4n^2 h2 ))

Question 6

What is reduced mass, when is it used and how is it calculated?

Answer 6

The reduced mass is essentially a method of treating two seperate masses as one mass, being a weighted average of the two. It is used when analysing a system of two orbiting bodies, as both bodies will orbit eachother at the same time. It is calculated from:

m_r=(m_1*m_2)/(m_1+m_2 )

Question 7

What are the polar coordinates used in atomic orbitals and how to we adapt the Schrodinger equation to reflect these?

Answer 7

The polar coordinates are the distance from the nucleus (r), the angle of rotation around the first axis (theta) and the angle of rotation around the second (epsilon).
We change the schrodinger equation to recieve this by adapting it to accept 3d coordinates.

Question 8

What are the 2 conditions under which solutions can be found from the adapted schrodinger equation for polar coordinates?

Answer 8

1. The function R(r), which is the component of probability in the radius, must tend to 0 as r increases, as the probability of finding an electron further out decreases due to higher potential energy.
2. The angles must be periodic and can only have valued between 0 and 2*pi

Question 9

What is the equation for the total energy of an orbital?

Answer 9

E = (-1/(4piepsilon))(4pime^4/2n^2h^2)

Question 10

What is the equation for the magnitude of angular momentum in an orbital?

Answer 10

L=(√(l(l+1) ) h/2π

Question 11

What is the angular momentum quantum number?

Answer 11

The angular momentum quantum number is an integer that has n different values for the n^th energy level (ranging from 0 to n-1). It represents the angular momentum in the current orbital, and changes as an electron moves between energy levels.

Question 12

What is the equation for a component of angular momentum?

Answer 12

L_z = (m_l h)/2π

Question 13

What is the magnetic quantum number?

Answer 13

The orbital magnetic quantum number determines the orientation of the angular momentum of the electron, quantified to be relative to each energy level. It can have any value from −l to l, with each representing a different orientation of the angular motion.

Question 14

What are the ranges of angular momentum quantum numbers and magnetic quantum numbers for a energy level n?

Answer 14

l = (0, 1, 2, …, n-1)
m_l = (-l, …, l)

Question 15

Why cant the magnitude of a component of angular momentum have itself the magnitude of angular momentum?

Answer 15

The uncertainity in the momentum would be 0, and therefore it would be infinite in the position. This isn’t possible as we know the electron is localised to a specific field of space, leading to an inconsistency.

Question 16

Given a principle quantum number n, what are the values l and m_l can take?

Answer 16

Given n, l = {0, 1, 2,…, n-1)
m_l = (-l, …, l

Question 17

What do quantum numbers describe about the behaviour of an electron, describing the effect of each quantum number?

Answer 17

They describe an electron’s behaviour inside an atom, for example n represents distance from the atom, l represents angular momentum (and as such the shape of the orbit), and m_l represents the way this angular momentum is oriented.

Question 18

What is the name for one configuration of quantum numbers?

Answer 18

A quantum state

Question 19

What are the letters associated with different angular momentum quantum numbers?

Answer 19

l = 0 - s state
l = 1 - p state
l = 2 - d state
l = 3 - f state
l = 4 - g state
l = 5 - h state
and so on…

Question 20

What is the name of the region of space associated with each energy level (n)?

Answer 20

n = 1 - K shell
n = 2 - L shell
n = 3 - M shell
n = 4 - N shell

Question 21

What is spin angular momentum?

Answer 21

Spin angular momentum is thought of as the clockwise/anti-clockwise rotation of an electron as it orbits the nucleus. It isn’t actually, as the electron is not a particle, however it is an accurate enough description.

Question 22

What is the Zeeman effect and what causes it?

Answer 22

The Zeeman effect is the splitting of the emission lines of atoms, and occurs due to the magnetic field produced by electron spin interfering with the electromagnetic waves produced when an electron changes energy levels.

Question 23

How is electron spin calculated?

Answer 23

S=±h/4π

Question 24

How is the z component of electron spin calculated?

Answer 24

S_z=(m_s)h/2π

Question 25

What are the names for positive and negative spin?

Answer 25

Spin up and Spin down

Question 26

How can orbital angular momentum and electron spin be combined?

Answer 26

Electron spin is just the spin angular momentum, so can be combined with the orbital angular momentum to produce the total angular momentum. This is given in the formula: J=L+S

Question 27

How is total angular momentum found using the total angular momentum quantum number?

Answer 27

J=(√(j(j+1) )h/2π

Question 28

What is the total angular momentum quantum number and what are its possible values?

Answer 28

It is a quantized version of the total angular momentum, and can have possible values of j=|l±1/2|

Question 29

What is the definition of a current, and what is the equation?

Answer 29

A current is any motion of charge from one region to another, and is given as I = dQ/dt

Question 30

What causes power from a source to be transmitted to components?

Answer 30

The source does work to accelerate the charged particles in the field, with this energy being given to electric components in order to activate them.

Question 31

How is the equation for current derived?

Answer 31

By analysing an infinitely small cross-section of a conductor and counting the number of charges passing through it at any instant in time.

Question 32

What happens to the current when there is no electric field?

Answer 32

When there is no electric field, there is still a slight random movement in charge, however random movements average out to 0 over time, so there is no net current flow.

Question 33

What is the thermal velocity of an electron?

Answer 33

The thermal velocity of an electron is the velocity an electron has when existing in a conductor of temperature T. This causes random movements of electrons in the conductor.

Question 34

How is the thermal velocity calculated?

Answer 34

v_tℎ=√((3k_B T)/m)

Question 35

What happens to an electron's velocity when an electric field is applied?

Answer 35

When an electric field is applied, the random motion of the electrons in the direction of the electric field is combined, meaning that while in all other directions the total velocity is just the thermal velocity, in the direction of the electric field the thermal velocity and field acceleration combine to cause an overall drift.

Question 36

What causes energy loss in a conductor, and in what form is this energy lost?

Answer 36

Energy is lost in a conductor when electrons collide with the conductor's ions. When this occurs, the ions vibrate as a result of this energy gain, and as such there is an increase of heat energy, with this energy essentially being lost to heat.

Question 37

What is drift velocity and how is it calculated?

Answer 37

Drift velocity is the average velocity of a group of charges in a conductor, and is given as = +(qE/m)τ

Question 38

Why do components turn on even though electrons are conducted slowly?

Answer 38

There are electrons evenly distributed throughout a conductor, and the electric field travels around the speed of light, meaning that the component will recieve electrons instantly.

Question 39

What is the electron concentration, and how is it found for a copper conductor?

Answer 39

The electron concentration is the number of electrons in a conductor. When copper is used to conduct electrons, each copper atom within the conductor gives one free electron. This means that the electron concentration is the same as the number of atoms in the conductor, and is given as: n=N_ap/A, where n is the number of electrons, N_a is avogadros constant, p is the density of the material and A is the cross-section of the conducting wire.

Question 40

What is an alternative equation for current in terms of the number of electrons in a conductor?

Answer 40

I = nqAv_d Where I is the current, n is the number of electrons, q is the charge on the electron A is the cross-sectional area and v_d is the drift velocity.

Question 41

What is the current density and how is it calculated?

Answer 41

Current density is the flow of current per unit of area in a conductor. It can be calculated by its definition as J = I/A and can also be found as J = nq^2t(E/m), where n is the number of electrons, q is the charge on an electron, t is the mean free time between collisions, E is the strength of the electric field and m is the mass of the electron.

Question 42

What is conductivity, how does it relate to the strength of an electric field, and how does it relate to thermal conduction?

Answer 42

Conductivity is a measure of the current density as a result of the applied field strength. A denser current indicates a higher conductivity than a less-dense current from the same field strength. A material with a high conductivity will have a high thermal conductivity, as they lose heat easily which allows electrons to flow better.

Question 43

How is conductivity calculated?

Answer 43

Conductivity is the current density per electric field strength, and is therefore calculated using: σ=J/E

Question 44

What is resistivity?

Answer 44

Resistivity is the inverse of conductivity, and is the electric field strength that is required for a specific current density. If a conductor is poor at conducting, it will require a greater field strength to achieve the same current density.

Question 45

How is resistivity calculated?

Answer 45

Resistivity is the inverse of conductivity, and is the field strength per current density. Therefore is calculated as: p = 1/σ = E/J

Question 46

What is resistance, and how is it calculated?

Answer 46

Resistance is a measure of the amount of resistivity per unit of area for a conductor over the entire length of the conductor. It is calculated as: R = (Lp/A)

Question 47

What is Ohm's law, and how is it derived?

Answer 47

Ohm's law is the idea that current density depends on the field strength, or in other words, the amount of current in a conductor depends on the energy put into it. Analysing the field in a conductor in terms of the potential difference, the equation is V = EL. Knowing that the current is given as I = JA, we can reach I/A = V/Lp. This rearranges to V=I(Lp/A)=IR.

Question 48

For which charges does Ohm's Law apply?

Answer 48

Ohm's law applies to all charges that are free to move, as current is simply the flow of charge, positive or negative in any form not just electrons.